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"These personnel will support the operation of intelligence, surveillance, and reconnaissance aircraft for missions over northern Nigeria and the surrounding area," Obama said in the letter.
"The force will remain in Chad until its support in resolving the kidnapping situation is no longer required," he said.
The girls were taken in April from a boarding school close to Nigeria's border with Cameroon, Niger and Chad in a sparsely populated region. Their whereabouts are unknown.
US surveillance aircraft have been flying over remote areas of northeast Nigeria for two weeks, and the Pentagon struck an agreement last weekend to allow it to share intelligence directly with the Nigerian government.
The US government has also sent officials from the State Department and the FBI to Nigeria to help in the search.